The effect of stiffness and mass on coupled oscillations in a phononic crystal

Abstract

Insight into phononic bandgap formation is presented using a first principles-type approach where phononic lattices are treated as coupled oscillators connected via massless tethers. The stiffness of the tethers and the mass of the oscillator are varied and their influences on the bandgap formation are deduced. This analysis is reinforced by conducting numerical simulations to examine the modes bounding the bandgap and highlighting the effect of the above parameters. The analysis presented here not only sheds light on the origins of gap formation, but also allows one to define design rules for wide phononic gaps and maximum gap-to-midgap ratios.

Approaching the intrinsic quality factor limit for micromechanical bulk acoustic resonators using phononic crystal tethers

“…The measured f×Q product for all PnC tether WE-BARs (red circles), and all straight-beam tether WE-BARs (green triangles) in this study compared to previously reported values (blue squares) 1, 21, 22 , as a function of frequency. A maximum f×Q of 1.2×10 13 Hz is measured at 282 MHz.…”

“…19, 20 The ability to control acoustic phonon dispersion enables the design of acoustic/phononic bandgaps 19, 20 that can be used as tethers or shields to efficiently confine energy in a phonon cavity or resonator. 15, 21–26 In such devices, acoustic propagation is mitigated by using multiple repeating units to create a phononic crystal (PnC) that has a transmission bandgap. Several of these studies have focused on improving the Q of acoustic Fabry-Pérot resonators.…”

“…14–16 This technique can be implemented to improve the Q of micromechanical resonators, by using PnCs as the tethers. Simple mass-link PnCs with 1-dimensional (1-D) connectivity used as the tethers have been found to be effective in recent analyses 21–23 and preliminary experiments. 24–26 However, the use of piezoelectric resonators with metal electrodes introduces additional dissipation within the materials and at their interfaces, thereby limiting the improvement resulting from the PnC tethers.…”

Ultra-high frequency, high Q/volume micromechanical resonators in a planar AlN phononic crystal

“…The details of this analysis can be found elsewhere. 28 Simulations also show that by removing two rows of PnCs and creating a W-2 cavity, there is one transverse mode at 1119 MHz (out-of-plane displacement) inside the bandgap. This frequency is within the bandgap of the PnC and therefore allows for the confinement of energy.…”

Demonstration of acoustic waveguiding and tight bending in phononic crystals

“…Given that the manipulation of transmitted and/or blocked frequencies depends on the lattice symmetry and the shape and spacing of the inclusions, various types of lattices, such as square, 14 triangular, honeycomb, and hexagonal, 15 with various inclusions ranging from simple geometrical circular inclusions to fractal 16 inclusions, have been studied using different numerical approaches, including plane-wave expansion, finite-difference time-domain, and finite-element method (FEM). [17][18][19] As the miniaturization trend of RF acoustic circuits continues, there is an ever-increasing need for the efficient guiding of acoustic signals to various extremities of chips. In the quest for chip real estate optimization, the guiding requirements often involve routing waves through a 90 bend.…”